Back after a long hiatus on Cap’s Whiteboard, today I talk a little about a combinatorics problem I’ve been playing with. I’m hoping to classify Latin squares which satsify a strong symmetry condition.

This time on Cap’s Whiteboard, a quickie gem about combinatorial geometry. Is it possible to start with a rectangle, neither of whose sides has integral length, and cut it into smaller rectangular pieces, each of which has at least one integral side?

It has been said (by the mathematician Alain Connes) that you cannot understand the integers unless you understand this.

This time on Cap’s Whiteboard, some remarks on an undeservedly-little-known proof that there are infinitely many prime numbers, which works by treating as a topological space, a bit of ingenuity due to Furstenburg (as far as I know).